Exercises: Fractions (1.4)
Exercises: Find Equivalent Fractions
Instructions: For questions 1-4, find three fractions equivalent to the given fraction. Show your work, using figures or algebra.
1. [latex]\frac{3}{8}[/latex]
Solution
[latex]\frac{6}{16},\frac{9}{24},\frac{12}{32}[/latex] (Answers may vary)
2. [latex]\frac{5}{8}[/latex]
3. [latex]\frac{5}{9}[/latex]
Solution
[latex]\frac{10}{18},\frac{15}{27},\frac{20}{36}[/latex] (Answers may vary)
4. [latex]\frac{1}{8}[/latex]
Exercises: Simplify Fractions
Instructions: For questions 5-14, simplify.
5. [latex]-\frac{40}{88}[/latex]
Solution
[latex]-\frac{5}{11}[/latex]
6. [latex]-\frac{63}{99}[/latex]
7. [latex]-\frac{108}{63}[/latex]
Solution
[latex]-\frac{12}{7}[/latex]
8. [latex]-\frac{104}{48}[/latex]
9. [latex]\frac{120}{252}[/latex]
Solution
[latex]\frac{10}{21}[/latex]
10. [latex]\frac{182}{294}[/latex]
11. [latex]-\frac{3x}{12y}[/latex]
Solution
[latex]-\frac{x}{4y}[/latex]
12. [latex]-\frac{4x}{32y}[/latex]
13. [latex]\frac{14{x}^{2}}{21y}[/latex]
Solution
[latex]\frac{2{x}^{2}}{3y}[/latex]
14. [latex]\frac{24a}{32{b}^{2}}[/latex]
Exercises: Multiply Fractions
Instructions: For questions 15-30, multiply.
15. [latex]\frac{3}{4}\cdot\frac{9}{10}[/latex]
Solution
[latex]\frac{27}{40}[/latex]
16. [latex]\frac{4}{5}\cdot\frac{2}{7}[/latex]
17. [latex]-\frac{2}{3}\left(-\frac{3}{8}\right)[/latex]
Solution
[latex]\frac{1}{4}[/latex]
18. [latex]-\frac{3}{4}\left(-\frac{4}{9}\right)[/latex]
19. [latex]-\frac{5}{9}\cdot\frac{3}{10}[/latex]
Solution
[latex]-\frac{1}{6}[/latex]
20. [latex]-\frac{3}{8}\cdot\frac{4}{15}[/latex]
21. [latex]\left(-\frac{14}{15}\right)\left(\frac{9}{20}\right)[/latex]
Solution
[latex]-\frac{21}{50}[/latex]
22. [latex]\left(-\frac{9}{10}\right)\left(\frac{25}{33}\right)[/latex]
23. [latex]\left(-\frac{63}{84}\right)\left(-\frac{44}{90}\right)[/latex]
Solution
[latex]\frac{11}{30}[/latex]
24. [latex]\left(-\frac{63}{60}\right)\left(-\frac{40}{88}\right)[/latex]
25. [latex]4\cdot\frac{5}{11}[/latex]
Solution
[latex]\frac{20}{11}[/latex]
26. [latex]5\cdot\frac{8}{3}[/latex]
27. [latex]\frac{3}{7}\cdot21n[/latex]
Solution
[latex]9n[/latex]
28. [latex]\frac{5}{6}\cdot30m[/latex]
29. [latex](-8)\left(\frac{17}{4}\right)[/latex]
Solution
[latex]-34[/latex]
30. [latex](-1)\left(-\frac{6}{7}\right)[/latex]
Exercises: Divide Fractions
Instructions: For questions 31-44, divide.
31. [latex]\frac{3}{4}\div\frac{2}{3}[/latex]
Solution
[latex]\frac{9}{8}[/latex]
32. [latex]\frac{4}{5}\div\frac{3}{4}[/latex]
33. [latex]-\frac{7}{9}\div\left(-\frac{7}{4}\right)[/latex]
Solution
[latex]1[/latex]
34. [latex]-\frac{5}{6}\div\left(-\frac{5}{6}\right)[/latex]
35. [latex]\frac{3}{4}\div\frac{x}{11}[/latex]
Solution
[latex]\frac{33}{4x}[/latex]
36. [latex]\frac{2}{5}\div\frac{y}{9}[/latex]
37. [latex]\frac{5}{18}\div\left(-\frac{15}{24}\right)[/latex]
Solution
[latex]-\frac{4}{9}[/latex]
38. [latex]\frac{7}{18}\div\left(-\frac{14}{27}\right)[/latex]
39. [latex]\frac{8u}{15}\div\frac{12v}{25}[/latex]
Solution
[latex]\frac{10u}{9v}[/latex]
40. [latex]\frac{12r}{25}\div\frac{18s}{35}[/latex]
41. [latex]-5\div\frac{1}{2}[/latex]
Solution
[latex]-10[/latex]
42. [latex]-3\div\frac{1}{4}[/latex]
43. [latex]\frac{3}{4}\div\left(-12\right)[/latex]
Solution
[latex]-\frac{1}{16}[/latex]
44. [latex]-15\div\left(-\frac{5}{3}\right)[/latex]
Exercises: Simplify by Dividing
Instructions: For questions 45-50, simplify.
45. [latex]\displaystyle\frac{-\frac{8}{21}}{\frac{12}{35}}[/latex]
Solution
[latex]-\frac{10}{9}[/latex]
46. [latex]\displaystyle\frac{-\frac{9}{16}}{\frac{33}{40}}[/latex]
47. [latex]\displaystyle\frac{-\frac{4}{5}}{2}[/latex]
Solution
[latex]-\frac{2}{5}[/latex]
48. [latex]\displaystyle\frac{5}{\frac{3}{10}}[/latex]
49. [latex]\displaystyle\frac{\frac{m}{3}}{\frac{n}{2}}[/latex]
Solution
[latex]\frac{2m}{3n}[/latex]
50. [latex]\displaystyle\frac{-\frac{3}{8}}{-\frac{y}{12}}[/latex]
Exercises: Simplify Expressions Written with a Fraction Bar
Instructions: For questions 51-70, simplify.
51. [latex]\frac{22+3}{10}[/latex]
Solution
[latex]\frac{5}{2}[/latex]
52. [latex]\frac{19-4}{6}[/latex]
53. [latex]\frac{48}{24-15}[/latex]
Solution
[latex]\frac{16}{3}[/latex]
54. [latex]\frac{46}{4+4}[/latex]
55. [latex]\frac{-6+6}{8+4}[/latex]
Solution
[latex]0[/latex]
56. [latex]\frac{-6+3}{17-8}[/latex]
57. [latex]\frac{4\cdot3}{6\cdot6}[/latex]
Solution
[latex]\frac{1}{3}[/latex]
58. [latex]\frac{6\cdot6}{9\cdot2}[/latex]
59. [latex]\frac{{4}^{2}-1}{25}[/latex]
Solution
[latex]\frac{3}{5}[/latex]
60. [latex]\frac{{7}^{2}+1}{60}[/latex]
61. [latex]\frac{8\cdot3+2\cdot9}{14+3}[/latex]
Solution
[latex]2\frac{8}{17}[/latex]
62. [latex]\frac{9\cdot6-4\cdot7}{22+3}[/latex]
63. [latex]\frac{5\cdot6-3\cdot4}{4\cdot5-2\cdot3}[/latex]
Solution
[latex]\frac{3}{5}[/latex]
64. [latex]\frac{8\cdot9-7\cdot6}{5\cdot6-9\cdot2}[/latex]
65. [latex]\frac{{5}^{2}-{3}^{2}}{3-5}[/latex]
Solution
[latex]-8[/latex]
66. [latex]\frac{{6}^{2}-{4}^{2}}{4-6}[/latex]
67. [latex]\frac{7\cdot4-2(8-5)}{9\cdot3-3\cdot5}[/latex]
Solution
[latex]\frac{11}{6}[/latex]
68. [latex]\frac{9\cdot7-3(12-8)}{8\cdot7-6\cdot6}[/latex]
69. [latex]\frac{9(8-2)-3(15-7)}{6(7-1)-3(17-9)}[/latex]
Solution
[latex]\frac{5}{2}[/latex]
70. [latex]\frac{8(9-2)-4(14-9)}{7(8-3)-3(16-9)}[/latex]
Exercises: Translate Phrases to Expressions with Fractions
Instructions: For questions 71-74, translate each English phrase into an algebraic expression.
71. the quotient of [latex]r[/latex] and the sum of [latex]s[/latex] and [latex]10[/latex]
Solution
[latex]\frac{r}{s+10}[/latex]
72. the quotient of [latex]A[/latex] and the difference of [latex]3[/latex] and [latex]B[/latex]
73. the quotient of the difference of [latex]x[/latex] and [latex]y[/latex], and [latex]-3[/latex]
Solution
[latex]\frac{x-y}{-3}[/latex]
74. the quotient of the sum of [latex]m[/latex] and [latex]n[/latex], and [latex]4q[/latex]
Exercises: Everyday Math
Instructions: For questions 75-78, answer the given everyday math word problems.
75. Baking. A recipe for chocolate chip cookies calls for [latex]\frac{3}{4}[/latex] cup brown sugar. Imelda wants to double the recipe.
a. How much brown sugar will Imelda need? Show your calculation.
b. Measuring cups usually come in sets of [latex]\frac{1}{4},\frac{1}{3},\frac{1}{2},\text{ and }1[/latex] cup. Draw a diagram to show two different ways that Imelda could measure the brown sugar needed to double the cookie recipe.
Solution
a.[latex]1\frac{1}{2}[/latex] cups
b. Answers will vary
76. Baking. Nina is making [latex]4[/latex] pans of fudge to serve after a music recital. For each pan, she needs [latex]\frac{2}{3}[/latex] cup of condensed milk.
a. How much condensed milk will Nina need? Show your calculation.
b. Measuring cups usually come in sets of [latex]\frac{1}{4},\frac{1}{3},\frac{1}{2},\text{ and }1[/latex] cup. Draw a diagram to show two different ways that Nina could measure the condensed milk needed for [latex]4[/latex] pans of fudge.
77. Portions. Don purchased a bulk package of candy that weighs [latex]5[/latex] pounds. He wants to sell the candy in little bags that hold [latex]\frac{1}{4}[/latex] pound. How many little bags of candy can he fill from the bulk package?
Solution
[latex]20[/latex] bags
78. Portions. Kristen has [latex]\frac{3}{4}[/latex] yards of ribbon that she wants to cut into [latex]6[/latex] equal parts to make hair ribbons for her daughter’s [latex]6[/latex] dolls. How long will each doll’s hair ribbon be?
Exercises: Writing Exercises
Instructions: For questions 79-82, answer the given writing exercises.
79. Rafael wanted to order half a medium pizza at a restaurant. The waiter told him that a medium pizza could be cut into [latex]6[/latex] or [latex]8[/latex] slices. Would he prefer [latex]3[/latex] out of [latex]6[/latex] slices or [latex]4[/latex] out of [latex]8[/latex] slices? Rafael replied that since he wasn’t very hungry, he would prefer [latex]3[/latex] out of [latex]6[/latex] slices. Explain what is wrong with Rafael’s reasoning.
Solution
Answers may vary
80. Give an example from everyday life that demonstrates how [latex]\frac{1}{2}\cdot\frac{2}{3}[/latex] is [latex]\frac{1}{3}[/latex].
81. Explain how you find the reciprocal of a fraction.
Solution
Answers may vary
82. Explain how you find the reciprocal of a negative number.
Exercises: Add Fractions with a Common Denominator
Instructions: For questions 83-92, add.
83. [latex]\frac{6}{13}+\frac{5}{13}[/latex]
Solution
[latex]\frac{11}{13}[/latex]
84. [latex]\frac{4}{15}+\frac{7}{15}[/latex]
85. [latex]\frac{x}{4}+\frac{3}{4}[/latex]
Solution
[latex]\frac{x+3}{4}[/latex]
86. [latex]\frac{8}{q}+\frac{6}{q}[/latex]
87. [latex]-\frac{3}{16}+\left(-\frac{7}{16}\right)[/latex]
Solution
[latex]-\frac{5}{8}[/latex]
88. [latex]-\frac{5}{16}+\left(-\frac{9}{16}\right)[/latex]
89. [latex]-\frac{8}{17}+\frac{15}{17}[/latex]
Solution
[latex]\frac{7}{17}[/latex]
90. [latex]-\frac{9}{19}+\frac{17}{19}[/latex]
91. [latex]\frac{6}{13}+\left(-\frac{10}{13}\right)+\left(-\frac{12}{13}\right)[/latex]
Solution
[latex]-\frac{16}{13}[/latex]
92. [latex]\frac{5}{12}+\left(-\frac{7}{12}\right)+\left(-\frac{11}{12}\right)[/latex]
Exercises: Subtract Fractions with a Common Denominator
Instructions: For questions 93-106, subtract.
93. [latex]\frac{11}{15}-\frac{7}{15}[/latex]
Solution
[latex]\frac{4}{15}[/latex]
94. [latex]\frac{9}{13}-\frac{4}{13}[/latex]
95. [latex]\frac{11}{12}-\frac{5}{12}[/latex]
Solution
[latex]\frac{1}{2}[/latex]
96. [latex]\frac{7}{12}-\frac{5}{12}[/latex]
97. [latex]\frac{19}{21}-\frac{4}{21}[/latex]
Solution
[latex]\frac{5}{7}[/latex]
98. [latex]\frac{17}{21}-\frac{8}{21}[/latex]
99. [latex]\frac{5y}{8}-\frac{7}{8}[/latex]
Solution
[latex]\frac{5y-7}{8}[/latex]
100. [latex]\frac{11z}{13}-\frac{8}{13}[/latex]
101. [latex]-\frac{23}{u}-\frac{15}{u}[/latex]
Solution
[latex]-\frac{38}{u}[/latex]
102. [latex]-\frac{29}{v}-\frac{26}{v}[/latex]
103. [latex]-\frac{3}{5}-\left(-\frac{4}{5}\right)[/latex]
Solution
[latex]\frac{1}{5}[/latex]
104. [latex]-\frac{3}{7}-\left(-\frac{5}{7}\right)[/latex]
105. [latex]-\frac{7}{9}-\left(-\frac{5}{9}\right)[/latex]
Solution
[latex]-\frac{2}{9}[/latex]
106. [latex]-\frac{8}{11}-\left(-\frac{5}{11}\right)[/latex]
Exercises: Mixed Practice
Instructions: For questions 107-114, simplify.
107. [latex]-\frac{5}{18}\cdot\frac{9}{10}[/latex]
Solution
[latex]-\frac{1}{4}[/latex]
108. [latex]-\frac{3}{14}\cdot\frac{7}{12}[/latex]
109. [latex]\frac{n}{5}-\frac{4}{5}[/latex]
Solution
[latex]\frac{n-4}{5}[/latex]
110. [latex]\frac{6}{11}-\frac{s}{11}[/latex]
111. [latex]-\frac{7}{24}+\frac{2}{24}[/latex]
Solution
[latex]-\frac{5}{24}[/latex]
112. [latex]-\frac{5}{18}+\frac{1}{18}[/latex]
113. [latex]\frac{8}{15}\div\frac{12}{5}[/latex]
Solution
[latex]\frac{2}{9}[/latex]
114. [latex]\frac{7}{12}\div\frac{9}{28}[/latex]
Exercises: Add or Subtract Fractions with Different Denominators
Instructions: For questions 115-138, add or subtract.
115. [latex]\frac{1}{2}+\frac{1}{7}[/latex]
Solution
[latex]\frac{9}{14}[/latex]
116. [latex]\frac{1}{3}+\frac{1}{8}[/latex]
117. [latex]\frac{1}{3}-\left(-\frac{1}{9}\right)[/latex]
Solution
[latex]\frac{4}{9}[/latex]
118. [latex]\frac{1}{4}-\left(-\frac{1}{8}\right)[/latex]
119. [latex]\frac{7}{12}+\frac{5}{8}[/latex]
Solution
[latex]\frac{29}{24}[/latex]
120. [latex]\frac{5}{12}+\frac{3}{8}[/latex]
121. [latex]\frac{7}{12}-\frac{9}{16}[/latex]
Solution
[latex]\frac{1}{48}[/latex]
122. [latex]\frac{7}{16}-\frac{5}{12}[/latex]
123. [latex]\frac{2}{3}-\frac{3}{8}[/latex]
Solution
[latex]\frac{7}{24}[/latex]
124. [latex]\frac{5}{6}-\frac{3}{4}[/latex]
125. [latex]-\frac{11}{30}+\frac{27}{40}[/latex]
Solution
[latex]\frac{37}{120}[/latex]
126. [latex]-\frac{9}{20}+\frac{17}{30}[/latex]
127. [latex]-\frac{13}{30}+\frac{25}{42}[/latex]
Solution
[latex]\frac{17}{105}[/latex]
128. [latex]-\frac{23}{30}+\frac{5}{48}[/latex]
129. [latex]-\frac{39}{56}-\frac{22}{35}[/latex]
Solution
[latex]-\frac{53}{40}[/latex]
130. [latex]-\frac{33}{49}-\frac{18}{35}[/latex]
131. [latex]-\frac{2}{3}-\left(-\frac{3}{4}\right)[/latex]
Solution
[latex]\frac{1}{12}[/latex]
132. [latex]-\frac{3}{4}-\left(-\frac{4}{5}\right)[/latex]
133. [latex]1+\frac{7}{8}[/latex]
Solution
[latex]\frac{15}{8}[/latex]
134. [latex]1-\frac{3}{10}[/latex]
135. [latex]\frac{x}{3}+\frac{1}{4}[/latex]
Solution
[latex]\frac{4x+3}{12}[/latex]
136. [latex]\frac{y}{2}+\frac{2}{3}[/latex]
137. [latex]\frac{y}{4}-\frac{3}{5}[/latex]
Solution
[latex]\frac{4y-12}{20}[/latex]
138. [latex]\frac{x}{5}-\frac{1}{4}[/latex]
Exercises: Mixed Practice
Instructions: For questions 139-152, simplify.
139.
a. [latex]\frac{2}{3}+\frac{1}{6}[/latex]
b. [latex]\frac{2}{3}\div\frac{1}{6}[/latex]
Solution
a. [latex]\frac{5}{6}[/latex]
b. [latex]4[/latex]
140.
a. [latex]-\frac{2}{5}-\frac{1}{8}[/latex]
b. [latex]-\frac{2}{5}\cdot\frac{1}{8}[/latex]
141.
a. [latex]\frac{5n}{6}\div\frac{8}{15}[/latex]
b. [latex]\frac{5n}{6}-\frac{8}{15}[/latex]
Solution
a. [latex]\frac{25n}{16}[/latex]
b. [latex]\frac{25n-16}{30}[/latex]
142.
a. [latex]\frac{3a}{8}\div\frac{7}{12}[/latex]
b. [latex]\frac{3a}{8}-\frac{7}{12}[/latex]
143. [latex]-\frac{3}{8}\div\left(-\frac{3}{10}\right)[/latex]
Solution
[latex]\frac{5}{4}[/latex]
144. [latex]-\frac{5}{12}\div\left(-\frac{5}{9}\right)[/latex]
145. [latex]-\frac{3}{8}+\frac{5}{12}[/latex]
Solution
[latex]\frac{1}{24}[/latex]
146. [latex]-\frac{1}{8}+\frac{7}{12}[/latex]
147. [latex]\frac{5}{6}-\frac{1}{9}[/latex]
Solution
[latex]\frac{13}{18}[/latex]
148. [latex]\frac{5}{9}-\frac{1}{6}[/latex]
149. [latex]-\frac{7}{15}-\frac{y}{4}[/latex]
Solution
[latex]\frac{-28-15y}{60}[/latex]
150. [latex]-\frac{3}{8}-\frac{x}{11}[/latex]
151. [latex]\frac{11}{12a}\cdot\frac{9a}{16}[/latex]
Solution
[latex]\frac{33}{64}[/latex]
152. [latex]\frac{10y}{13}\cdot\frac{8}{15y}[/latex]
Exercises: Use the Order of Operations to Simplify Complex Fractions
Instructions: For questions 153-174, simplify.
153. [latex]\frac{{2}^{3}+{4}^{2}}{{\left(\frac{2}{3}\right)}^{2}}[/latex]
Solution
[latex]54[/latex]
154. [latex]\frac{{3}^{3}-{3}^{2}}{{\left(\frac{3}{4}\right)}^{2}}[/latex]
155. [latex]\frac{{\left(\frac{3}{5}\right)}^{2}}{{\left(\frac{3}{7}\right)}^{2}}[/latex]
Solution
[latex]\frac{49}{25}[/latex]
156. [latex]\frac{{\left(\frac{3}{4}\right)}^{2}}{{\left(\frac{5}{8}\right)}^{2}}[/latex]
157. [latex]\frac{2}{\frac{1}{3}+\frac{1}{5}}[/latex]
Solution
[latex]\frac{15}{4}[/latex]
158. [latex]\frac{5}{\frac{1}{4}+\frac{1}{3}}[/latex]
159. [latex]\displaystyle\frac{\frac{7}{8}-\frac{2}{3}}{\frac{1}{2}+\frac{3}{8}}[/latex]
Solution
[latex]\frac{5}{21}[/latex]
160. [latex]\displaystyle\frac{\frac{3}{4}-\frac{3}{5}}{\frac{1}{4}+\frac{2}{5}}[/latex]
161. [latex]\frac{1}{2}+\frac{2}{3}\cdot\frac{5}{12}[/latex]
Solution
[latex]\frac{7}{9}[/latex]
162. [latex]\frac{1}{3}+\frac{2}{5}\cdot\frac{3}{4}[/latex]
163. [latex]1-\frac{3}{5}\div\frac{1}{10}[/latex]
Solution
[latex]-5[/latex]
164. [latex]1-\frac{5}{6}\div\frac{1}{12}[/latex]
165. [latex]\frac{2}{3}+\frac{1}{6}+\frac{3}{4}[/latex]
Solution
[latex]\frac{19}{12}[/latex]
166. [latex]\frac{2}{3}+\frac{1}{4}+\frac{3}{5}[/latex]
167. [latex]\frac{3}{8}-\frac{1}{6}+\frac{3}{4}[/latex]
Solution
[latex]\frac{23}{24}[/latex]
168. [latex]\frac{2}{5}+\frac{5}{8}-\frac{3}{4}[/latex]
169. [latex]12\left(\frac{9}{20}-\frac{4}{15}\right)[/latex]
Solution
[latex]\frac{11}{5}[/latex]
170. [latex]8\left(\frac{15}{16}-\frac{5}{6}\right)[/latex]
171. [latex]\displaystyle\frac{\frac{5}{8}+\frac{1}{6}}{\frac{19}{24}}[/latex]
Solution
[latex]1[/latex]
172. [latex]\displaystyle\frac{\frac{1}{6}+\frac{3}{10}}{\frac{14}{30}}[/latex]
173. [latex]\left(\frac{5}{9}+\frac{1}{6}\right)\div\left(\frac{2}{3}-\frac{1}{2}\right)[/latex]
Solution
[latex]\frac{13}{3}[/latex]
174. [latex]\left(\frac{3}{4}+\frac{1}{6}\right)\div\left(\frac{5}{8}-\frac{1}{3}\right)[/latex]
Exercises: Evaluate Variable Expressions with Fractions
Instructions: For questions 175-184, evaluate.
175. [latex]x+\left(-\frac{5}{6}\right)[/latex] when
a. [latex]x=\frac{1}{3}[/latex]
b. [latex]x=-\frac{1}{6}[/latex]
Solution
a. [latex]-\frac{1}{2}[/latex]
b. [latex]-1[/latex]
176. [latex]x+\left(-\frac{11}{12}\right)[/latex] when
a. [latex]x=\frac{11}{12}[/latex]
b. [latex]x=\frac{3}{4}[/latex]
177. [latex]x-\frac{2}{5}[/latex] when
a. [latex]x=\frac{3}{5}[/latex]
b. [latex]x=-\frac{3}{5}[/latex]
Solution
a. [latex]\frac{1}{5}[/latex]
b. [latex]-1[/latex]
178. [latex]x-\frac{1}{3}[/latex] when
a. [latex]x=\frac{2}{3}[/latex]
b. [latex]x=-\frac{2}{3}[/latex]
179. [latex]\frac{7}{10}-w[/latex] when
a. [latex]w=\frac{1}{2}[/latex]
b. [latex]w=-\frac{1}{2}[/latex]
Solution
a. [latex]\frac{1}{5}[/latex]
b. [latex]\frac{6}{5}[/latex]
180. [latex]\frac{5}{12}-w[/latex] when
a. [latex]w=\frac{1}{4}[/latex]
b. [latex]w=-\frac{1}{4}[/latex]
181. [latex]2{x}^{2}{y}^{3}[/latex] when [latex]x=-\frac{2}{3}[/latex] and [latex]y=-\frac{1}{2}[/latex]
Solution
[latex]-\frac{1}{9}[/latex]
182. [latex]8{u}^{2}{v}^{3}[/latex] when [latex]u=-\frac{3}{4}[/latex] and [latex]v=-\frac{1}{2}[/latex]
183. [latex]\frac{a+b}{a-b}[/latex] when [latex]a=-3,b=8[/latex]
Solution
[latex]-\frac{5}{11}[/latex]
184. [latex]\frac{r-s}{r+s}[/latex] when [latex]r=10,s=-5[/latex]
Exercises: Everyday Math
Instructions: For questions 185-186, answer the given everyday math word problems.
185. Decorating. Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs [latex]\frac{1}{2}[/latex] yard of print fabric and [latex]\frac{3}{8}[/latex] yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?
Solution
[latex]\frac{7}{8}[/latex] yard
186. Baking. Vanessa is baking chocolate chip cookies and oatmeal cookies. She needs [latex]\frac{1}{2}[/latex] cup of sugar for the chocolate chip cookies and [latex]\frac{1}{4}[/latex] of sugar for the oatmeal cookies. How much sugar does she need altogether?
Exercises: Writing Exercises
Instructions: For questions 187-188, answer the given writing exercises.
187. Why do you need a common denominator to add or subtract fractions? Explain.
Solution
Answers may vary
188. How do you find the LCD of [latex]2[/latex] fractions?
